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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.stat.descriptive.moment;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.25"></a>
<FONT color="green">026</FONT>    <a name="line.26"></a>
<FONT color="green">027</FONT>    /**<a name="line.27"></a>
<FONT color="green">028</FONT>     * Computes the skewness of the available values.<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;p&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * We use the following (unbiased) formula to define skewness:&lt;/p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * skewness = [n / (n -1) (n - 2)] sum[(x_i - mean)^3] / std^3 &lt;/p&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * where n is the number of values, mean is the {@link Mean} and std is the<a name="line.34"></a>
<FONT color="green">035</FONT>     * {@link StandardDeviation} &lt;/p&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;p&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * &lt;strong&gt;Note that this implementation is not synchronized.&lt;/strong&gt; If<a name="line.37"></a>
<FONT color="green">038</FONT>     * multiple threads access an instance of this class concurrently, and at least<a name="line.38"></a>
<FONT color="green">039</FONT>     * one of the threads invokes the &lt;code&gt;increment()&lt;/code&gt; or<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;code&gt;clear()&lt;/code&gt; method, it must be synchronized externally. &lt;/p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     *<a name="line.41"></a>
<FONT color="green">042</FONT>     * @version $Id: Skewness.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.42"></a>
<FONT color="green">043</FONT>     */<a name="line.43"></a>
<FONT color="green">044</FONT>    public class Skewness extends AbstractStorelessUnivariateStatistic implements Serializable {<a name="line.44"></a>
<FONT color="green">045</FONT>    <a name="line.45"></a>
<FONT color="green">046</FONT>        /** Serializable version identifier */<a name="line.46"></a>
<FONT color="green">047</FONT>        private static final long serialVersionUID = 7101857578996691352L;<a name="line.47"></a>
<FONT color="green">048</FONT>    <a name="line.48"></a>
<FONT color="green">049</FONT>        /** Third moment on which this statistic is based */<a name="line.49"></a>
<FONT color="green">050</FONT>        protected ThirdMoment moment = null;<a name="line.50"></a>
<FONT color="green">051</FONT>    <a name="line.51"></a>
<FONT color="green">052</FONT>         /**<a name="line.52"></a>
<FONT color="green">053</FONT>         * Determines whether or not this statistic can be incremented or cleared.<a name="line.53"></a>
<FONT color="green">054</FONT>         * &lt;p&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>         * Statistics based on (constructed from) external moments cannot<a name="line.55"></a>
<FONT color="green">056</FONT>         * be incremented or cleared.&lt;/p&gt;<a name="line.56"></a>
<FONT color="green">057</FONT>        */<a name="line.57"></a>
<FONT color="green">058</FONT>        protected boolean incMoment;<a name="line.58"></a>
<FONT color="green">059</FONT>    <a name="line.59"></a>
<FONT color="green">060</FONT>        /**<a name="line.60"></a>
<FONT color="green">061</FONT>         * Constructs a Skewness<a name="line.61"></a>
<FONT color="green">062</FONT>         */<a name="line.62"></a>
<FONT color="green">063</FONT>        public Skewness() {<a name="line.63"></a>
<FONT color="green">064</FONT>            incMoment = true;<a name="line.64"></a>
<FONT color="green">065</FONT>            moment = new ThirdMoment();<a name="line.65"></a>
<FONT color="green">066</FONT>        }<a name="line.66"></a>
<FONT color="green">067</FONT>    <a name="line.67"></a>
<FONT color="green">068</FONT>        /**<a name="line.68"></a>
<FONT color="green">069</FONT>         * Constructs a Skewness with an external moment<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param m3 external moment<a name="line.70"></a>
<FONT color="green">071</FONT>         */<a name="line.71"></a>
<FONT color="green">072</FONT>        public Skewness(final ThirdMoment m3) {<a name="line.72"></a>
<FONT color="green">073</FONT>            incMoment = false;<a name="line.73"></a>
<FONT color="green">074</FONT>            this.moment = m3;<a name="line.74"></a>
<FONT color="green">075</FONT>        }<a name="line.75"></a>
<FONT color="green">076</FONT>    <a name="line.76"></a>
<FONT color="green">077</FONT>        /**<a name="line.77"></a>
<FONT color="green">078</FONT>         * Copy constructor, creates a new {@code Skewness} identical<a name="line.78"></a>
<FONT color="green">079</FONT>         * to the {@code original}<a name="line.79"></a>
<FONT color="green">080</FONT>         *<a name="line.80"></a>
<FONT color="green">081</FONT>         * @param original the {@code Skewness} instance to copy<a name="line.81"></a>
<FONT color="green">082</FONT>         * @throws NullArgumentException if original is null<a name="line.82"></a>
<FONT color="green">083</FONT>         */<a name="line.83"></a>
<FONT color="green">084</FONT>        public Skewness(Skewness original) throws NullArgumentException {<a name="line.84"></a>
<FONT color="green">085</FONT>            copy(original, this);<a name="line.85"></a>
<FONT color="green">086</FONT>        }<a name="line.86"></a>
<FONT color="green">087</FONT>    <a name="line.87"></a>
<FONT color="green">088</FONT>        /**<a name="line.88"></a>
<FONT color="green">089</FONT>         * {@inheritDoc}<a name="line.89"></a>
<FONT color="green">090</FONT>         * &lt;p&gt;Note that when {@link #Skewness(ThirdMoment)} is used to<a name="line.90"></a>
<FONT color="green">091</FONT>         * create a Skewness, this method does nothing. In that case, the<a name="line.91"></a>
<FONT color="green">092</FONT>         * ThirdMoment should be incremented directly.&lt;/p&gt;<a name="line.92"></a>
<FONT color="green">093</FONT>         */<a name="line.93"></a>
<FONT color="green">094</FONT>        @Override<a name="line.94"></a>
<FONT color="green">095</FONT>        public void increment(final double d) {<a name="line.95"></a>
<FONT color="green">096</FONT>            if (incMoment) {<a name="line.96"></a>
<FONT color="green">097</FONT>                moment.increment(d);<a name="line.97"></a>
<FONT color="green">098</FONT>            }<a name="line.98"></a>
<FONT color="green">099</FONT>        }<a name="line.99"></a>
<FONT color="green">100</FONT>    <a name="line.100"></a>
<FONT color="green">101</FONT>        /**<a name="line.101"></a>
<FONT color="green">102</FONT>         * Returns the value of the statistic based on the values that have been added.<a name="line.102"></a>
<FONT color="green">103</FONT>         * &lt;p&gt;<a name="line.103"></a>
<FONT color="green">104</FONT>         * See {@link Skewness} for the definition used in the computation.&lt;/p&gt;<a name="line.104"></a>
<FONT color="green">105</FONT>         *<a name="line.105"></a>
<FONT color="green">106</FONT>         * @return the skewness of the available values.<a name="line.106"></a>
<FONT color="green">107</FONT>         */<a name="line.107"></a>
<FONT color="green">108</FONT>        @Override<a name="line.108"></a>
<FONT color="green">109</FONT>        public double getResult() {<a name="line.109"></a>
<FONT color="green">110</FONT>    <a name="line.110"></a>
<FONT color="green">111</FONT>            if (moment.n &lt; 3) {<a name="line.111"></a>
<FONT color="green">112</FONT>                return Double.NaN;<a name="line.112"></a>
<FONT color="green">113</FONT>            }<a name="line.113"></a>
<FONT color="green">114</FONT>            double variance = moment.m2 / (moment.n - 1);<a name="line.114"></a>
<FONT color="green">115</FONT>            if (variance &lt; 10E-20) {<a name="line.115"></a>
<FONT color="green">116</FONT>                return 0.0d;<a name="line.116"></a>
<FONT color="green">117</FONT>            } else {<a name="line.117"></a>
<FONT color="green">118</FONT>                double n0 = moment.getN();<a name="line.118"></a>
<FONT color="green">119</FONT>                return  (n0 * moment.m3) /<a name="line.119"></a>
<FONT color="green">120</FONT>                ((n0 - 1) * (n0 -2) * FastMath.sqrt(variance) * variance);<a name="line.120"></a>
<FONT color="green">121</FONT>            }<a name="line.121"></a>
<FONT color="green">122</FONT>        }<a name="line.122"></a>
<FONT color="green">123</FONT>    <a name="line.123"></a>
<FONT color="green">124</FONT>        /**<a name="line.124"></a>
<FONT color="green">125</FONT>         * {@inheritDoc}<a name="line.125"></a>
<FONT color="green">126</FONT>         */<a name="line.126"></a>
<FONT color="green">127</FONT>        public long getN() {<a name="line.127"></a>
<FONT color="green">128</FONT>            return moment.getN();<a name="line.128"></a>
<FONT color="green">129</FONT>        }<a name="line.129"></a>
<FONT color="green">130</FONT>    <a name="line.130"></a>
<FONT color="green">131</FONT>        /**<a name="line.131"></a>
<FONT color="green">132</FONT>         * {@inheritDoc}<a name="line.132"></a>
<FONT color="green">133</FONT>         */<a name="line.133"></a>
<FONT color="green">134</FONT>        @Override<a name="line.134"></a>
<FONT color="green">135</FONT>        public void clear() {<a name="line.135"></a>
<FONT color="green">136</FONT>            if (incMoment) {<a name="line.136"></a>
<FONT color="green">137</FONT>                moment.clear();<a name="line.137"></a>
<FONT color="green">138</FONT>            }<a name="line.138"></a>
<FONT color="green">139</FONT>        }<a name="line.139"></a>
<FONT color="green">140</FONT>    <a name="line.140"></a>
<FONT color="green">141</FONT>        /**<a name="line.141"></a>
<FONT color="green">142</FONT>         * Returns the Skewness of the entries in the specifed portion of the<a name="line.142"></a>
<FONT color="green">143</FONT>         * input array.<a name="line.143"></a>
<FONT color="green">144</FONT>         * &lt;p&gt;<a name="line.144"></a>
<FONT color="green">145</FONT>         * See {@link Skewness} for the definition used in the computation.&lt;/p&gt;<a name="line.145"></a>
<FONT color="green">146</FONT>         * &lt;p&gt;<a name="line.146"></a>
<FONT color="green">147</FONT>         * Throws &lt;code&gt;IllegalArgumentException&lt;/code&gt; if the array is null.&lt;/p&gt;<a name="line.147"></a>
<FONT color="green">148</FONT>         *<a name="line.148"></a>
<FONT color="green">149</FONT>         * @param values the input array<a name="line.149"></a>
<FONT color="green">150</FONT>         * @param begin the index of the first array element to include<a name="line.150"></a>
<FONT color="green">151</FONT>         * @param length the number of elements to include<a name="line.151"></a>
<FONT color="green">152</FONT>         * @return the skewness of the values or Double.NaN if length is less than<a name="line.152"></a>
<FONT color="green">153</FONT>         * 3<a name="line.153"></a>
<FONT color="green">154</FONT>         * @throws MathIllegalArgumentException if the array is null or the array index<a name="line.154"></a>
<FONT color="green">155</FONT>         *  parameters are not valid<a name="line.155"></a>
<FONT color="green">156</FONT>         */<a name="line.156"></a>
<FONT color="green">157</FONT>        @Override<a name="line.157"></a>
<FONT color="green">158</FONT>        public double evaluate(final double[] values,final int begin,<a name="line.158"></a>
<FONT color="green">159</FONT>                final int length) throws MathIllegalArgumentException {<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>            // Initialize the skewness<a name="line.161"></a>
<FONT color="green">162</FONT>            double skew = Double.NaN;<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>            if (test(values, begin, length) &amp;&amp; length &gt; 2 ){<a name="line.164"></a>
<FONT color="green">165</FONT>                Mean mean = new Mean();<a name="line.165"></a>
<FONT color="green">166</FONT>                // Get the mean and the standard deviation<a name="line.166"></a>
<FONT color="green">167</FONT>                double m = mean.evaluate(values, begin, length);<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>                // Calc the std, this is implemented here instead<a name="line.169"></a>
<FONT color="green">170</FONT>                // of using the standardDeviation method eliminate<a name="line.170"></a>
<FONT color="green">171</FONT>                // a duplicate pass to get the mean<a name="line.171"></a>
<FONT color="green">172</FONT>                double accum = 0.0;<a name="line.172"></a>
<FONT color="green">173</FONT>                double accum2 = 0.0;<a name="line.173"></a>
<FONT color="green">174</FONT>                for (int i = begin; i &lt; begin + length; i++) {<a name="line.174"></a>
<FONT color="green">175</FONT>                    final double d = values[i] - m;<a name="line.175"></a>
<FONT color="green">176</FONT>                    accum  += d * d;<a name="line.176"></a>
<FONT color="green">177</FONT>                    accum2 += d;<a name="line.177"></a>
<FONT color="green">178</FONT>                }<a name="line.178"></a>
<FONT color="green">179</FONT>                final double variance = (accum - (accum2 * accum2 / length)) / (length - 1);<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>                double accum3 = 0.0;<a name="line.181"></a>
<FONT color="green">182</FONT>                for (int i = begin; i &lt; begin + length; i++) {<a name="line.182"></a>
<FONT color="green">183</FONT>                    final double d = values[i] - m;<a name="line.183"></a>
<FONT color="green">184</FONT>                    accum3 += d * d * d;<a name="line.184"></a>
<FONT color="green">185</FONT>                }<a name="line.185"></a>
<FONT color="green">186</FONT>                accum3 /= variance * FastMath.sqrt(variance);<a name="line.186"></a>
<FONT color="green">187</FONT>    <a name="line.187"></a>
<FONT color="green">188</FONT>                // Get N<a name="line.188"></a>
<FONT color="green">189</FONT>                double n0 = length;<a name="line.189"></a>
<FONT color="green">190</FONT>    <a name="line.190"></a>
<FONT color="green">191</FONT>                // Calculate skewness<a name="line.191"></a>
<FONT color="green">192</FONT>                skew = (n0 / ((n0 - 1) * (n0 - 2))) * accum3;<a name="line.192"></a>
<FONT color="green">193</FONT>            }<a name="line.193"></a>
<FONT color="green">194</FONT>            return skew;<a name="line.194"></a>
<FONT color="green">195</FONT>        }<a name="line.195"></a>
<FONT color="green">196</FONT>    <a name="line.196"></a>
<FONT color="green">197</FONT>        /**<a name="line.197"></a>
<FONT color="green">198</FONT>         * {@inheritDoc}<a name="line.198"></a>
<FONT color="green">199</FONT>         */<a name="line.199"></a>
<FONT color="green">200</FONT>        @Override<a name="line.200"></a>
<FONT color="green">201</FONT>        public Skewness copy() {<a name="line.201"></a>
<FONT color="green">202</FONT>            Skewness result = new Skewness();<a name="line.202"></a>
<FONT color="green">203</FONT>            // No try-catch or advertised exception because args are guaranteed non-null<a name="line.203"></a>
<FONT color="green">204</FONT>            copy(this, result);<a name="line.204"></a>
<FONT color="green">205</FONT>            return result;<a name="line.205"></a>
<FONT color="green">206</FONT>        }<a name="line.206"></a>
<FONT color="green">207</FONT>    <a name="line.207"></a>
<FONT color="green">208</FONT>        /**<a name="line.208"></a>
<FONT color="green">209</FONT>         * Copies source to dest.<a name="line.209"></a>
<FONT color="green">210</FONT>         * &lt;p&gt;Neither source nor dest can be null.&lt;/p&gt;<a name="line.210"></a>
<FONT color="green">211</FONT>         *<a name="line.211"></a>
<FONT color="green">212</FONT>         * @param source Skewness to copy<a name="line.212"></a>
<FONT color="green">213</FONT>         * @param dest Skewness to copy to<a name="line.213"></a>
<FONT color="green">214</FONT>         * @throws NullArgumentException if either source or dest is null<a name="line.214"></a>
<FONT color="green">215</FONT>         */<a name="line.215"></a>
<FONT color="green">216</FONT>        public static void copy(Skewness source, Skewness dest)<a name="line.216"></a>
<FONT color="green">217</FONT>            throws NullArgumentException {<a name="line.217"></a>
<FONT color="green">218</FONT>            MathUtils.checkNotNull(source);<a name="line.218"></a>
<FONT color="green">219</FONT>            MathUtils.checkNotNull(dest);<a name="line.219"></a>
<FONT color="green">220</FONT>            dest.setData(source.getDataRef());<a name="line.220"></a>
<FONT color="green">221</FONT>            dest.moment = new ThirdMoment(source.moment.copy());<a name="line.221"></a>
<FONT color="green">222</FONT>            dest.incMoment = source.incMoment;<a name="line.222"></a>
<FONT color="green">223</FONT>        }<a name="line.223"></a>
<FONT color="green">224</FONT>    }<a name="line.224"></a>




























































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